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The Post-Newtonian and MPM Formalisms

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Applied General Relativity

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Abstract

The idea of the post-Newtonian formalism is to employ the fact that in the solar system velocities of astronomical bodies are small and gravitational fields are weak. The PN-formalism is a slow motion, weak field approximation to Einstein’s theory of gravity.

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Notes

  1. 1.

    Note, that the basic variable in the paper by Damour and Iyer (1991a) is \(\bar h^{\alpha \beta } = - h^{\alpha \beta }\).

References

  • Blanchet, L., 1995: Second post-Newtonian generation of gravitational radiation, Phys. Rev., D 51, pp. 2559–2583.

    Article  ADS  Google Scholar 

  • Blanchet, L., 1998: On the multipole expansion of the gravitational field, Class. Quantum Grav., 15, pp. 1971–1999.

    Article  ADS  MathSciNet  Google Scholar 

  • Blanchet, L., 2006: Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Relativity 9, 4.

    MATH  Google Scholar 

  • Blanchet, L., 2014: Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Relativity 17: 2. https://doi.org/10.12942/lrr-2014-2.

    MATH  Google Scholar 

  • Blanchet, L., Damour, T., 1986: Radiative gravitational fields in general relativity: I. General structure of the field outside the source. Phil. Trans. Roy. Soc. London, A320, pp. 379–430.

    MATH  Google Scholar 

  • Blanchet, L., Damour, T., 1989: Post-Newtonian generation of gravitational waves, Ann. Inst. H. PoincarĂ©, 50, pp. 377–408.

    ADS  MathSciNet  MATH  Google Scholar 

  • Blanchet, L., Faye, G., 2001a: General relativistic dynamics of compact binaries at the third post-Newtonian order, Phys. Rev., D 63, 062005-1-43.

    Google Scholar 

  • Chandrasekhar, S., 1965: The Post-Newtonian Equations of Hydrodynamics in General Relativity, Astrophys. J., 142, pp. 1488–1512.

    Article  ADS  MathSciNet  Google Scholar 

  • Chandrasekhar, S., Nutku, Y., 1996: The Second Post-Newtonian Equations of Hydrodynamics in General Relativity, Astrophys. J., 158, pp. 55–79.

    Article  ADS  MathSciNet  Google Scholar 

  • Chandrasekhar, S., Esposito, F., 1970 : The 2\(\frac 12\) Post-Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity, Astrophys. J., 160, pp. 153–179.

    Article  ADS  MathSciNet  Google Scholar 

  • Damour, T., Iyer, B.R., 1991a: Post-Newtonian generation of gravitational waves. II: The spin moments, Ann. Inst. Henri PoincarĂ© 54, pp. 115–164.

    MathSciNet  MATH  Google Scholar 

  • Damour, T., Soffel, M., Xu, C., 1991: General-relativistic celestial mechanics. I. Method and definition of reference systems, Phys. Rev., D 43, pp. 3273–3307 (DSX-I).

    Article  ADS  MathSciNet  Google Scholar 

  • de Sitter, S., 1916: On Einstein’s Theory of Gravitation and its Astronomical Consequences, Mon. Not. Roy. Astr. Soc., 77, pp. 155–184.

    Article  ADS  Google Scholar 

  • Droste, J., 1916: Versl. K. Akad. Wet. Amsterdam 19, pp. 447–455.

    Google Scholar 

  • Einstein, A., 1915: Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie, Sitzungsberichte Preuss. Akad. Wiss. Berlin, 1915, II, pp. 831–839.

    Google Scholar 

  • Fock, V.A., 1959: The Theory of Space, Time and Gravitation, Pergamon, Oxford.

    Google Scholar 

  • Lorentz, H.A., Droste, J., 1917: Versl. K. Akad. Wet. Amsterdam 26, 392 (part I); 26, 649 (part II), English translation in H.A. Lorentz, Collected Papers, edited by P. Zeeman and A. D. Fokker (Nijhoff, The Hague, 1937), Vol. V, pp. 330–355.

    Google Scholar 

  • Thorne, K., 1980: Multipole expansions of gravitational radiation, Rev. Mod. Phys., 52, pp. 299–339.

    Article  ADS  MathSciNet  Google Scholar 

  • Zschocke, S., 2014: A detailed proof of the fundamental theorem of STF multipole expansion in linearized gravity, Int. J. Mod. Phys., D 23, 1450003.

    Article  ADS  MathSciNet  Google Scholar 

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Soffel, M.H., Han, WB. (2019). The Post-Newtonian and MPM Formalisms. In: Applied General Relativity. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-030-19673-8_7

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